1
Effect of alkyl group substituents on the thermal
and enzymatic degradation of poly (n-alkyl acrylates)
J. P. Mahalik and Giridhar Madras∗
Department of Chemical Engineering, Indian Institute of Science, Bangalore-12
Abstract
The effect of alkyl group substituents on the thermal degradation kinetics of poly (n-alkyl
acrylate) was investigated in pyrolysis and in solution. The activation energies for the
pyrolytic degradation of poly (n-butyl acrylate) (PBA), poly (ethyl acrylate) (PEA), and
poly (methyl acrylate) (PMA), determined by the Friedman's technique, were 150, 170
and 203 kJ/mol, respectively. For the thermal degradation of the polymers in solution, a
continuous distribution kinetic model was used to determine the random chain
degradation rate coefficients. The activation energies, determined from the temperature
dependence of the rate coefficients, for PBA, PEA and PMA in solution were 109, 117,
and 138 kJ/mol, respectively. This indicates that the variation of the activation energies
with chain length of the substituent in the polymer is similar to degradation both by
pyrolysis and in solution, though the values obtained are lower for degradation in
solution. The enzymatic degradation of these polymers was also investigated at different
temperatures with various enzymes (Novozym 435, Lipolase and Porcine Pancreas) in
different solvents. A continuous distribution kinetic model was used to evaluate the
polymer chain end scission rate coefficient. The degradation rates were highest when the
acrylates were degraded in presence of Porcine Pancreas in toluene at 50 0C.
Keywords: poly (n-alkyl) acrylates, group substituents, thermal degradation, activation
energy, continuous distribution kinetics, enzymatic degradation, Lipases
∗
To whom the correspondence should be addressed, Tel: 091-80-22932321, Fax: 091-80-23600683.
Email: giridhar@chemeng.iisc.ernet.in
2
Introduction
Poly (acrylates) have wide commercial application in paints and coatings, paper
industry, adhesives and sealing compound, textile and leather industry. Among poly
(acrylates), poly (n-butyl acrylate) (PBA), poly (ethyl acrylate) (PEA), and poly (methyl
acrylate) (PMA) are widely used. The disposal of these synthetic polymers has stimulated
several investigations in the degradation of acrylates.
Several investigators1-7 have proposed that the mechanism of pyrolytic
degradation of PMA involves random homolytic scission followed by a series of
intramolecular and intermolecular transfer reactions. The pyrolytic degradation of PMA
and PEA8 yields gaseous products, the corresponding alcohol, monomer, and small
amounts of methacrylate esters. A detailed thermal degradation mechanism of PEA9 and
PBA10, 11 has been proposed. The mechanism of pyrolytic degradation of poly (ethyl, npropyl, isopropyl, n-butyl, and 2-ethylhexyl) acrylate12,
13
is similar to the degradation
mechanism of PMA5, 6.
While the degradation of poly (n-alkyl acrylates) by pyrolysis has been the subject
of many reports, the thermal degradation of poly (n-alkyl acrylates) in solution has not
been studied. Unlike pyrolysis, where problems like high melt viscosity, heat-transfer
resistance, and formation of undesirable byproducts15, 16 are encountered, degradation in
solution is advantageous because of the uniform temperature and heat transfer resulting in
degradation at lower temperatures compared to pyrolysis15, 16.
Other than thermal degradation, enzymatic degradation of synthetic polymers is a
promising technique. Among synthetic polymers, there have been reports on the
3
enzymatic degradation of polyesters by enzymes from various sources, mostly by lipases
and esterase17-20. Some enzymes such as lipases retain their activity even in waterinsoluble organic solvents because of their close proximity with a thin layer of water that
is tightly bound to the enzyme, which helps in retaining its conformation and activity21, 22.
Studies have also been conducted on the effect of solvent viscosity on the degradation of
polymers23. Very few investigations have been done on the enzymatic degradation of
poly (n-alkyl acrylates). The enzymatic degradation of 2-methylene-1, 3-dioxepane and
methyl acrylate copolymers using proteinase enzyme from earthworm has been
investigated24. However, the effect of lipase on homopolymers of poly (n-alkyl acrylate)
has not been investigated.
The objective of the present work is to study the effect of alkyl substituents on the
thermal degradation of poly (n-alkyl acrylates) both by pyrolysis and in solution. The
enzymatic degradation of these polymers have also been investigated with various
enzymes in different solvents at different temperatures.
Experimental Section
Materials: Methyl acrylate was obtained from Merck Chemicals (India), ethyl acrylate
was purchased from Rolex Chemicals (India) and n-butyl acrylate was obtained from S.
D. Fine Chemicals (India). The monomers were freed from inhibitors by washing with
5% caustic solution followed by washing with distilled water and then double distilled
under reduced pressure. The solvents, tetrahydrofuran (THF), benzene and toluene (all
from Merck Chemicals), were distilled and filtered prior to use. Benzoyl peroxide (S. D.
Fine Chemicals, India) was purified by dissolving it in chloroform followed by
precipitation in methanol. The immobilized enzymes, Novozym 435 and Lipolase
4
(commercial grades), were received as gifts from Novo Nordisk, Denmark. The free
enzyme from Porcine Pancreas (activity of 147 units/mg) was procured from Sigma
Aldrich. All enzymes were kept in a desiccator overnight to remove residual water.
Polymer synthesis: The yield of polymer using bulk polymerization technique was very
low (~10 % weight/weight), and, therefore, solution polymerization technique was used
to polymerize the acrylates, at 60 0C in benzene using benzoyl peroxide as initiator. An
initiator concentration of 1-2 g/L and monomer concentration of 40-60 volume % in
benzene was used to synthesize the polymers. The number average molecular weights of
the obtained poly (n-butyl, ethyl, and methyl) acrylate were found to be 320000, 435000,
and 350000, respectively, with polydispersities of 1.7, 1.4 and 1.4, respectively.
Pyrolysis Experiment: 15-20 mg of the polymer was pyrolysed in a nitrogen flow
environment (150 cm3 min-1) in a thermogravimetric analyzer (TGA) (Perkin-Elmer,
Pyris) at two different heating rates of 10 0C/min and 20 0C/min from 50 to 700 0C.
Experiments on thermal degradation in solution: The thermal degradation of PBA,
PEA, and PMA was investigated at various temperatures (270 –310 oC) at a constant
polymer concentration of 2 g/L in a high-pressure stirred batch reactor (Parr Model 4842)
with a capacity of 250 cm3. A predetermined volume of polymer solution in toluene was
initially fed to the reactor so that the reactor pressure reaches 25 bar at the desired
temperature25. The reactor temperature was controlled within + 1 oC of the set point with
a proportional-integral-derivative (PID) controller. Aliquots of 1 cm3 were collected at
regular
intervals
and
analyzed
in
Gel
Permeation
chromatography
(GPC).
5
Enzymatic Degradation Experiments: 15 ml solutions of PBA were prepared in four
different solvents: benzene, toluene, xylene and chlorobenzene. These solutions were
taken in four different screw cap culture tubes along with 0.015 grams of Novozym-435
and were placed in an incubator shaker water bath to maintain the temperature of the
reaction mixture at the desired value (50 0C) controlled by a PID controller (+ 0.1 0C).
Aliquots of 200 µ L were collected at regular intervals and analyzed in GPC. The
enzyme was removed from the sample by centrifugation before analysis. Similar
experiments were conducted to study the effect of various enzymes (Novozym-435,
Lipolase, and Porcine Pancreas) at different temperatures. Control experiments were
conducted in the absence of enzymes and no degradation was observed. Many
experiments were repeated thrice and the standard deviation in the rate coefficient was
found to be within 2%.
Molecular Weight Determination: The MWD of the samples were determined by gel
permeation chromatography (GPC, Waters, USA). The GPC consists of isocratic pump
(Waters 501) with automated gradient controller, Size exclusion columns (300 mm x 7.5
mm, Styragel HR 5E, HR3, and HR 0.5), differential refractometer (Waters R401) and a
data acquisition system in series. Samples were injected in a Rheodyne valve with a
sample loop of 50 µL and the refractive index was continuously monitored using a
differential refractive index detector and stored digitally. The chromatograph was
converted to molecular weight distribution using a universal calibration curve determined
using polystyrene standards (Polymer Lab, UK).
6
Theoretical Model
1. Thermal degradation by Pyrolysis
The Friedman technique is a common technique to study the pyrolytic behavior of
polymers26, wherein a plot of ln
dc
dt
with
1
is linear with a slope corresponding to
T
overall activation energy. In the above formula, c is the weight of the sample at any given
time t , and T represents the temperature of the sample at that time. In the Kissinger's
method27, ln
B
1
is plotted against , where Tm represents the temperature at the
2
Tm
Tm
maxima of the first derivative weight loss curves, and B is the heating rate.
2. Thermal Degradation in solution
The overall reaction for degradation can be
Kd
P ( x ') 
→ P ( x) + P ( x '− x)
(A)
where kd represents the degradation rate coefficient. The population balance equation for
the polymer undergoing reaction A in a batch reactor is28-30, with x (Molecular weight) as
the continuous variable
∞
∂p ( x, t )
= − kd ( x) p ( x, t ) + 2 p ( x ', t )kd ( x ')Ω( x, x ')dx '
∂t
x
(1)
The molecular weight distribution after thermal degradation does not show any specific
products and therefore the degradation is mostly by random chain scission, hence the
7
stoichiometric coefficient29,
30
is Ω( x, x ') = 1/ x ' . The degradation rate coefficient is
assumed to be linearly dependent30 on the molecular weight x ( kd ( x) = kd x ). Operating
∞
the moment x j p ( x, t )dx , equation (1) can be written as
0
dp ( j ) (t )
( j − 1) ( j +1)
= − kd
p
dt
( j + 1)
(2)
j = 0, 1, 2 correspond to the zeroth, first and second moments, respectively. The zeroth
moment is
dp (0)
= kd p (1)
dt
(3)
where p (0) and p (1) represents the molar concentration and mass concentration of the
polymer, respectively. According to the first moment, the mass concentration of the
polymer is constant throughout the reaction and thus using the definition of molecular
weight, M n =
p (1)
, equation (3) can be integrated and written as
p (0)
M n0
− 1 = M n 0 k d t = kt t
Mn
(4)
3. Enzymatic Degradation
The enzymes degrade the polymer of molecular weight x by specific chain end
scission to oligomers of a specific molecular weight xs and another polymer fragment.
The enzymatic degradation of poly (n-alkyl acrylate) is assumed to follow the following
steps. (A) Adsorption of enzyme on the polymer substrate. (B) Formation of transition
complex between polymer and enzyme. (C) Specific chain scission of the polymer. (D)
Desorption of the enzyme. Since, there is no hydrolysable linkage in the backbone of the
8
polymer; therefore the enzyme only hydrolyses the pendant acetate group in the side
chain of the polymer19. This can be represented in the form of the following reaction
scheme20
s
P(x)  k→
P(x-x s )+Q(x s )
(B)
Here, P ( x) represents the polymer of molecular weight x , Q ( xs ) represents the specific
product of MW, xs and p ( x, t ) and q (t ) represent concentrations of the polymer and the
specific product, respectively. For a well-mixed batch reactor, the population balance for
the polymer and the specific product is30
∞
∂p ( x, t )
= ks a (t ) p ( x′, t )Ω( x, ( x′ − xs ))dx′ − ks a (t ) p ( x, t )
∂t
x
(5a)
∞
∂q (t )
= k s a (t ) p ( x′, t )Ω( xs , x′)dx′
∂t
xs
(5b)
where a(t) is the activity of the enzyme and is assumed to decrease exponentially with
time, a (t ) = exp(− ket ) . For the specific chain end scission, the stoichiometric kernel29 Ω
(xs, x’) is equal to δ(xs, x). The rate coefficient, ks is assumed to be independent of the
molecular weight as it undergoes specific chain end scission. Applying the moment
operator,
∞
0
x j p ( x, t )dx , on equation (5a) and (5b), the following expressions are
obtained,
j
dp ( j )
= −k s a (t ) p ( j ) ( x, t ) + ks a (t ) (− xs ) j − d p (0) ( x, t )
dt
d =0
(6a)
dq ( j ) (t )
= ks a (t ) p (0) xsj
dt
(6b)
9
Equation (6b) shows the time variation of the specific product moments. The zeroth and
first moment represent the molar and mass concentration of the specific product and are
obtained by setting j = 0 and 1 in equation (6a) and (6b). This can be reduced to
dq (1) (t )
= ks exp(− ket ) xs p (0)
dt
(7)
Solving equation (7) with the initial condition q (1) (t = 0) =0 yields
ks xs p0(1)
q (t ) =
(1 − exp(−ket ) )
ke M n 0
(1)
As t
(8)
∝, when the enzyme is no more functional, equation (8) becomes
qs = q (1) (t → ∞) =
k s xs p0(1)
ke M n 0
(9)
where qs is the specific product concentration at long reaction times. Thus
qr (t ) =
q (1) (t )
= 1 − exp(− ke t )
q (1) (t → ∞)
(10)
Thus the rate coefficient, for the deactivation of the enzyme, ke , can be obtained by
plotting a semi-logarithm plot between 1 − qr (t ) and t, and, the scission rate coefficient
ks , can be obtained using equation (10).
Results and Discussion
Pyrolysis
The thermal degradation of PBA, PEA and PMA was investigated at two different
heating rates of 10 0C min-1 and 20 0C min-1 in a thermogravimetric analyzer (TGA) in a
nitrogen flow environment. Figure 1 shows the normalized weight loss profiles and the
differential thermogravimetric (DTG) curve for the degradation of the polymers at 10 0C
10
min-1. The activation energies determined by using Friedman’s plot (Figure 2) were 150,
170, 203 kJ/mol for the degradation of PBA, PEA, and PMA, respectively, at a heating
rate of 10 0C min-1. The Kissinger's method was also used to determine the activation
energy of PBA at different heating rates of 5, 10, 15, and 20 0C min-1, as shown in Figure
3. From the slope, the activation energy was determined to be 157 kJ/mol, which is
comparable with the value obtained by Friedman's method (150 kJ/mol) and the
activation energy (145-157 kJ/mol) reported by Hu et al.10.
Thermal Degradation in solution
Equation 4 shows that
M n0
− 1 varies linearly with time with a slope of rate
Mn
coefficient kt . Figures 4a-4c show the variation of number average molecular weight of
the polymers with time at various temperatures. The rate coefficients are obtained from
the slope after linear regression. For thermal degradation in solution, the rate coefficients
follows the order PMA> PEA> PBA, as shown in Figure 5. The activation energy for
these polymers was determined from the temperature dependence of the rate coefficients
by an Arrhenius plot (Figure 5). The average activation energies for the degradation of
PBA, PEA, and PMA were determined to be 109, 117, and 138 kJ/mol, respectively,
which is less than that obtained for pyrolysis.
The rate coefficient for degradation by pyrolysis is calculated based on TG weight
loss, while the rate coefficient for the thermal degradation in solution is derived by
population balances based on GPC data. Although the degradation mechanism of the
polymers, by both modes of thermal degradation is similar, the apparent activation energy
for pyrolytic degradation is higher than that of thermal degradation by solution. This can
be attributed to the evaporation of lower molecular weight leading to degradation of the
11
remaining higher molecular weight polymer molecules, unlike thermal degradation in
solution, where there is no loss of lower molecular weight polymer. This is consistent
with the observation for the degradation of other polymers. For example, the activation
energies for thermal degradation in solution31 for poly ( -caprolactone) (PCL) and
polyvinyl acetate (PVAC) are 106 and 56 kJ/mol, respectively, whereas the activation
energies for the degradation of PCL and PVAC by pyrolysis32 are 230-250 kJ/mol and
215-228 kJ/mol, respectively.
The variation of activation energy with chain length (Figure 6) is the same for
degradation by pyrolysis and in solution. The above trend can be explained in terms of
the delocalization of electrons33. The longer the alkyl group, higher is the delocalization
at the carbon atom linking two monomer units and thus more stable. When the alkyl
group is small, the delocalization of the electrons is less, so there are more tendencies for
the formation of radicals where the localization of electrons is less33. As the rate of
radical formation is directly related to the depropagation, the degradation rate follows the
order PMA > PEA > PBA, as shown in Figure 5.
Enzymatic degradation
The enzymatic degradation of PBA, PEA, and PMA was investigated with
different enzymes in different solvents at different temperatures. The effect of solvent on
the enzymatic degradation of PBA was investigated at 50 0C. The solvents, toluene,
chlorobenzene, benzene, and xylene were chosen based on their viscosity difference. The
enzymatic degradation of the polymers results in the formation of oligomers of
approximate number average molecular weight of 470. The concentration of the oligomer
increases with time while the concentration of the polymer decreases and gradually
12
reaches a constant value. The enzyme deactivation rate coefficient was determined by the
slope of semi logarithm plot of (1 − qr ) versus time (Figure 7) passing through the origin.
The rate coefficient, ks , was obtained using equation 9. The lines in Figure 7 are model
predictions that indicate that the model fits the experimental data satisfactorily. It has
been reported34 that the major effect of the organic solvent is on substrate binding, and
the catalytic steps are almost unaffected by the solvent. Therefore, enzyme degradability
can be quantified on the basis of thermodynamics of polymer solvation34 and the effect of
solvent on mass transfer20. However, the Huggins constant35 for polymer solvent
interaction for these acrylates do not differ much. Therefore, the major effect of the
solvent on the degradation is due to the viscosity of the solvent. Thus the overall
degradation coefficient ( kov =
ke
) is plotted against viscosity of the solvents in Figure 8.
ks
The rate coefficient decreases with increasing viscosity and thus can be attributed to the
decrease in diffusion rate of the polymer molecules to the enzymes resulting in lower
degradation20. Because the highest degradation rate of the polymers was obtained for
enzymatic degradation in toluene, it was chosen as the solvent for all other experiments.
The effect of the enzymes, Novozym 435, Lipolase and Porcine Pancreas, on the
degradation kinetics of PBA was investigated at 50 0C using toluene as the solvent
(Figure 9). The highest degradation was observed using Porcine Pancreas ( kov = 1.24)
while the degradation rates were lower with Lipolase ( kov = 0.88) and Novozym 435
( kov = 1.12). Because the highest degradation rate is obtained using Porcine Pancreas it
was chosen to study the effect of group substituents on the enzymatic degradation of poly
acrylates (PBA, PEA and PMA) at various temperatures (40, 50, and 60 0C) in toluene.
13
The effect of temperature on the degradation of PBA, PEA and PMA were obtained
similarly by plotting semi-logarithm plot of (1 − qr ) with time (Figures 10a-10c). The
overall degradation rate coefficient, kov , is plotted against temperature (Figure 11) for all
polymers. The optimum temperature for the enzymatic degradation of all polymers was
50 0C. At 40, 50 0C, the degradation rate followed the order PMA > PBA > PEA, while at
60 0C, the degradation rate followed the order PMA > PEA > PBA, which is similar to
the trend observed in pyrolysis/solution.
The rate coefficients obtained for the enzymatic degradation of poly (n-alkyl
acrylate) are comparable with poly ( -caprolactone) (kov= 18.8, in toluene at 60 0C, using
Novozym 435), poly (vinyl acetate) (kov =0.96, in toluene at 55 0C, using Novozym
435)19, and poly (bisphenol A carbonate) (kov=0.5, in toluene at 50 0C using Hog
Pancreas)20. The weight loss of PMA (Figure 10c) is comparable with that reported for
enzymatic degradation of PMA using crude enzyme from earthworm24. The optimum
temperature of 50 0C for degradation can be attributed to the conformation of the
enzymes and is similar to the optimum temperature obtained for the degradation of poly
(bisphenol A carbonate)20, poly ( -caprolactone)19 and poly (vinyl acetate)19.
Though the mechanism of thermal degradation through pyrolysis and in solution
is the same, the extent of degradation in both modes of degradation is different. The
degradation mechanism of poly (n-alkyl acrylates) has been widely reported5-13, and the
detailed account of the products formed is summarized5. The degradation product of
thermal degradation in solution is mostly poly (n-alkyl acrylate) of lower chain length.
However, the enzymatic degradation results in cleavage at pendant acetate group in the
side chain. The applicability of each of these techniques is different. Thermal
14
degradation provides the upper limit of the service temperature of the polymer.
Understanding biodegradability of the polymers is not only important for recycling of the
polymer in a low cost and eco-friendly way but also in biomedical applications. While
degradation by pyrolysis tends to nearly 100 % weight loss, with a variety of products, it
requires very high thermal energy. Degradation in solution has lower activation energy
but leads to only oligomers. Degradation of polyacrylates with enzymes leads to specific
products with only a small weight loss.
Conclusions
The thermal degradation of PBA, PEA, and PMA was investigated by pyrolysis and in
solution. Based on pyrolytic degradation studies it is found that the degradability of the
polymer decreases with increase in the alkyl group chain length of poly (n-alkyl acrylate).
A similar trend was observed for thermal degradation in solution, although the activation
energies obtained are lower than that observed for degradation by pyrolysis. The effect of
group substituents on the enzymatic degradation of acrylates (PMA, PEA and PBA) was
investigated using Porcine Pancreas in toluene at different temperatures (40, 50, 60 0C).
The optimum temperature for the degradation was found to be 50 0C. The order of
degradability of the polymers follows the same order as that of thermal degradation at
600C.
15
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20
Figure Captions
Figure 1: Weight loss profile and Differential weight loss profile (DTG) of poly (n-butyl,
ethyl, and methyl) acrylates at heating rate of 10 0C min-1.
Legends: , PBA; , PEA;
, PMA
Figure 2: Friedman plot to determine the activation energy for the degradation of poly (nbutyl, ethyl, and methyl) acrylate at heating rate of 10 0C min-1. The lines are fit by the
model. See Figure 1 for Legends
Figure 3: Kissinger's plot for determination of the activation energy for the degradation of
(PBA). The straight line represents the regressed fit.
Figure 4 Variation of number average molecular weight with time for the degradation of
(a) PBA (b) PEA (c) PMA. The rate coefficient, kd is obtained by linear regression. The
lines are fit by the model.
Legends: , 270oC; , 280oC;
, 290oC;
, 310oC
Figure 5: Arrhenius plot for the thermal degradation of Poly (n-alkyl) acrylate in solution
See Figure 2 for Legends
Figure 6: Activation energy as a function of number of carbon atoms in the alkyl group of
poly (n-alkyl) acrylate
Legends: , by Pyrolysis; , in solution
Figure 7: Variation of the mass fraction of the specific product with time by Novozym
435 at 50 0C in different solvents for the degradation of PBA. The lines are fit by the
model.
Legends: , Toluene; , Benzene;
, Xylene;
, Chlorobenzene
21
Figure 8: Dependence of composite rate coefficient kov , of the degradation of PBA on the
viscosity of the solvent using Novozym-435 at 50 0C in various solvents. See Figure 7 for
legends.
Figure 9: Variation of the mass fraction of the specific product with time in toluene at 50
0
C using different enzymes for the degradation of PBA. The lines are fit by the model.
Legends: , Novozym 435; , Lipolase;
, Porcine Pancreas
Figure 10: Variation of the mass fraction of the specific product with time in Toluene for
(a) PBA (b) PEA (c) PMA, using Porcine Pancreas. The lines are fit by the model.
Legends: , 40 0C; , 50 0C;
Figure 11: Variation of kov (=
, 60 0C
ks
) with temperature for enzymatic degradation of poly (nke
alkyl acrylate) in toluene using Porcine Pancreas. See Figure 1 for Legends
22
0.25
1.0
PEA
fractional mass retained
0.20
PBA
PMA
0.6
0.15
0.4
0.10
0.2
0.05
0.0
0.00
300
320
340
360
380
400
420
440
0
Temperature, C
Figure 1
460
480
500
520
Differential fractional weight loss
0.8
23
-6.2
-6.3
-6.4
-6.5
-6.6
ln(dc/dt)
-6.7
-6.8
-6.9
-7.0
-7.1
-7.2
-7.3
-7.4
-7.5
-7.6
0.00153
0.00154
0.00155
-1
1/T, K
Figure 2
0.00156
0.00157
24
-10.0
-10.2
-10.6
2
ln(B/Tm )
-10.4
-10.8
-11.0
-11.2
-11.4
1.43
1.44
1.45
1.46
1.47
3
1.48
10 /Tm, K
Figure 3
-1
1.49
1.50
1.51
25
4
(a)
(Mn0/Mn)-1
3
2
1
0
0
50
100
150
Reaction time, min
Figure 4
200
250
26
14
(b)
12
(Mn0/Mn)-1
10
8
6
4
2
0
0
50
100
150
Reaction time, min
Figure 4
200
250
27
22
20
(c)
18
16
(Mn0/Mn)-1
14
12
10
8
6
4
2
0
0
50
100
150
Reaction time, min
Figure 4
200
250
28
-2.0
-2.4
-2.8
-3.2
ln(kt)
-3.6
-4.0
-4.4
-4.8
-5.2
-5.6
0.00172
0.00176
0.00180
-1
1/T, K
Figure 5
0.00184
29
210
200
Activation Energy, kJ/mol
190
180
170
160
150
140
130
120
110
0
1
2
3
4
Number of carbon atoms in the alkyl group
Figure 6
5
30
0.0018
0.0016
0.0014
(1)
q (t)/p0
(1)
0.0012
0.0010
0.0008
6
5
(1)
s
-ln(1-q (t)/q )
0.0006
0.0004
0.0002
4
3
2
1
0
0
50
100
0.0000
0
50
100
150
200
Degradation time, hr
Figure 7
150
200
250
Degradation time, hr
250
300
31
1.15
1.10
1.05
kov
1.00
0.95
0.90
0.85
0.80
0.75
0.40
0.44
0.48
Viscosity, cP
Figure 8
0.52
0.56
32
0.0018
0.0016
0.0014
6
0.0010
5
0.0008
-ln(1-q (t)/qs)
(1)
q (t)/p0
(1)
0.0012
(1)
0.0006
0.0004
0.0002
4
3
2
1
0
0
50
100
200
250
Degradation time, hr
0.0000
0
50
100
150
200
Degradation time, hr
Figure 9
150
250
300
33
0.0018
(a)
0.0016
0.0014
0.0010
8
0.0008
7
6
s
-ln(1-q (t)/q )
(1)
q (t)/p0
(1)
0.0012
(1)
0.0006
0.0004
0.0002
5
4
3
2
1
0
0
50
100
0.0000
0
50
100
150
200
Degradation time, hr
Figure 10
150
200
250
Degradation time, hr
250
300
34
(b)
0.0012
0.0010
0.0006
7
6
s
-ln(1-q (t)/q)
(1)
q (t)/p0
(1)
0.0008
(1)
0.0004
0.0002
5
4
3
2
1
0
0
50
100
150
200
250
Degradation time, hr
0.0000
0
50
100
150
200
Degradation time, hr
Figure 10
250
300
350
35
0.0020
(c)
0.0018
0.0016
0.0014
0.0010
8
7
0.0008
6
s
-ln(1-q (t)/q )
(1)
q (t)/p0
(1)
0.0012
(1)
0.0006
0.0004
5
4
3
2
1
0
0.0002
0
50
100
150
200
250
Degradation time, hr
0.0000
0
50
100
150
200
Degradation time, hr
Figure 10
250
300
36
1.4
1.3
1.2
kov
1.1
1.0
0.9
0.8
0.7
0.6
40
50
60
0
Temperature, C
Figure 11